Effect of Non-linear Drag Term on Viscous Dissipation in a Fluid Saturated Porous Medium Channel with Various Boundary Conditions at Walls

Influence of quadratic drag term (the Forchheimer extension) is studied on viscous dissipation in a channel filled with a porous material bounded by two isothermal or isoflux walls. Two viscous dissipation models, the Darcy model and clear fluid compatible model, are examined. The differential transformation method (DTM) is applied to solve the non-linear Darcy-Brinkman-Forchheimer momentum equation to find an analytical approximate solution for dimensionless velocity and subsequently temperature profile as well as Nusselt number. The obtained results are validated with data available in the open literature and good agreements are observed. It was found that the Nusselt number is sensitive to the Forchheimer number under all conditions. At the isothermal boundary condition, increasing the value of the Forchheimer number leads to increase of the Nusselt number in the two models. With isoflux walls, the Forchheimer number increases the Nusselt number in Darcy model, while for clear fluid compatible model the effect of the form drag term on the Nusselt number substantially depends on the value of Darcy number.